1. Field of the Invention
The invention relates to a method for reconstructing a cross-section of an object from a number of X-ray projected images of the object and, more particularly, to a method of obtaining a cross-sectional reconstruction of the object that is uniquely determined.
2. Description of the Prior Art
The theory of reconstructing a three-dimensional or a two-dimensional cross-sectional view of an object from projections of the object has been known since at least 1917 when the Austrian mathematician J. Radon proved that objects can be reconstructed uniquely from the infinite set of all projections. However, full exploitation of such reconstruction techniques have had to await the arrival of modern computers and other developments in the art. Thus, it has been only recently that reconstruction techniques have been used to open a new era in the practice of medicine, allowing non-invasive procedures to be used to determine the internal structures of the human body.
Techniques for projecting the image of the internal structures (i.e., bones, organs, etc.) of the body are known. Many such techniques direct a diverging plurality of X-rays through the body to project an image of the internal structure onto a receiving element such as an X-ray plate. Invaluable as this technique is, it has long been difficult or impossible to distinguish one internal organ from another in view of their overlap on the film. This is particularly true when the X-ray density of one structure differs only slightly from the density of a neighboring one, as is often the case with a tumor and the tissue in which it is embedded.
One attempt to minimize this problem involves obtaining a number of X-ray projections from different angles to expose the internal organs in different relative positions. The pictures of the projected images are then viewed by an experienced physician who makes a qualitative determination of the internal structure of the patient so viewed.
A recent advance in the art builds upon the above technique by combining X-ray pictures through a mathematical procedure which yields a representation of the internal structure. With such vital information available, diagnosis can become more accurate, and more precise guidance can be given to the hand of the surgeon and to therapeutic radiation aimed at a tumor.
Thus, devices are on the market today which process X-ray projection data and produce a reconstruction (i.e., a finite dimensional approximation) of the actual mass distribution of a cross-section of the patient's body. These devices operate by directing X-rays through the patient's body in parallel rays as the patient (or the apparatus) is rotated in steps around a single axis. A photographic image is made at each step; that is, for each projection, structures in the patient's body lying in a plane perpendicular to the axis of rotation would be recorded on a single one-dimensional line. By measuring the X-ray density along that line on each image, the information from the desired plane is isolated. From this information a single two-dimensional plane is reconstructed and, if desired, the sequence of such planes are merely stacked to get a full three-dimensional picture.
Such devices utilize a collimator that is placed in front of an X-ray source to produce the parallel X-rays. An X-ray detector is positioned on the opposite side of the patient from the source and the collimator. The source, the collimator and the detector then scan across the patient in a direction perpendicular to the beam of the X-rays.
The Central Research Laboratories of EMI Limited of England have developed such a device for obtaining cross-sectional reconstructions of a patient's head. Known as the EMI Scanner, this instrument is designed primarily for scanning the brain. The system takes a projection at each of 180 different angles in one degree increments. Each projection is actually 160 different measurements so that 160 times 180 observations are entered into a computer for processing.
The next step in the method used by the EMI Scanner is the use of a computer-implemented algorithm which transforms the projection data into the desired reconstruction. For some time, the algorithm called the Algebraic Reconstruction Technique developed by Herman, Gordon, and Bender ("Algebraic Reconstruction Techniques [ART] for three-dimensional electron microscopy and X-ray photography", J. Theor. BIOL XXIX [1970], 471-481), was used to perform the desired transformation. Later the Convolution method, developed by Ramachandran and Lakshminarayanan ("Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms." Proc. Nat'l. Acad. Sci. USA LXVIII (1971), 2236-2240.), was implemented. Finally, the reconstruction is displayed on a cathode ray tube or T.V. screen.
However, despite the efforts of many who work in this art, the issue of uniqueness of reconstructions obtained by known prior art methods has remained an open and illusive question. As used herein, a uniquely determined reconstruction means that there is only one reconstruction which is in closest agreement with the projection data -- regardless of how "closeness" is defined.
It has long been known that any method of reconstruction is applied to a finite amount of real data (in contrast to the infinite number of mathematically precise projections required by Radon's theorem), and yields reconstructions that are at best only estimates of the object's actual structure. Moreover, the relative accuracy of various mathematical models has been found to depend on the nature of the data collected. Therefore, since it must be accepted that only a finite number of projections is practically available, the theoretical results which require more projection data are not applicable.
Additionally, experience has indicated, and supported by current mathematical analysis, that theretofore no test devised could predict the reliability of any particular reconstruction. More emphatically, this is not simply a question of being slightly off somewhere within the reconstruction, but important features, such as the existence and position of brain tumors, were inexplicably missing. In fact, 20 percent of the reconstructions produced by known devices have been considered incorrect. In short, present methods of obtaining reconstructions from projections lack the quality of being uniquely determined.
Heretofore, such inaccuracies and errors have been thought to be a consequence of the choice of the reconstruction algorithms, data collection, and/or the display of the information. Very little, if any, thought has been given, so far as is known, to the choice of angles from which the projections are taken and the relationship between the angles of each projection, the resolution in the projection data, and the resolution in the reconstruction as they affect the uniqueness of that reconstruction.